Does galaxy evolution proceed through the green valley via multiple pathways or as a single population? Motivated by recent results highlighting radically different evolutionary pathways between early- and late-type galaxies, we present results from a simple Bayesian approach to this problem wherein we model the star formation history (SFH) of a galaxy with two parameters, [t, \tau] and compare the predicted and observed optical and near-ultraviolet colours. We use a novel method to investigate the morphological differences between the most probable SFHs for both disc-like and smooth-like populations of galaxies, by using a sample of 126,316 galaxies (0.01 <z <0.25) with probabilistic estimates of morphology from Galaxy Zoo. We find a clear difference between the quenching timescales preferred by smooth- and disc-like galaxies, with three possible routes through the green valley dominated by smooth- (rapid timescales, attributed to major mergers), intermediate- (intermediate timescales, attributed to minor mergers and galaxy interactions) and disc-like (slow timescales, attributed to secular evolution) galaxies. We hypothesise that morphological changes occur in systems which have undergone quenching with an exponential timescale \tau <1.5 Gyr, in order for the evolution of galaxies in the green valley to match the ratio of smooth to disc galaxies observed in the red sequence. These rapid timescales are instrumental in the formation of the red sequence at earlier times; however we find that galaxies currently passing through the green valley typically do so at intermediate timescales.